Tedious endgames are one of the great joys of correspondence Chess. Just ride it out. Of course, you can negotiate with your opponent some sort of draw, if it really is going nowhere, or you might convince them to resign if they are playing a dead hand. There can be nothing done, however, for the individual who chooses to let an obviously lost position muck about for weeks in a pawn-shuffling endgame. Best to just let it slide.
Tedious End Game
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But your opponent was a piece up. He was the one that wanted to win, you couldn't do anything about it.
It was not at all a tedius end game. Since position was imbalanced some result was expected. With better play you could have won earlier. But you must learn to enjoy ending. Otherwise you will not improve. Sometime you have to play 20 moves to improve position of your king by one or two squares. Then you again plan and play many moves to bring it up. ( see examples of triangulation - how one plays many move to bring back same position ( !! ) with just move transfer and its effect). In your game around 34th move when you have queen on 7th rank and rook on open file you should plan to move king to avoid checks even if few pawns go. Once you can move rook to 8th or 7th rank game is over. You found position tedius because you were playing move to move without a plan. Once you make a plan and use it to win a drawish game it gives lot of satisfaction.
I have been stuck in a situation like this on a few occasions and i never really know what to do. Toward the end of this game, we both had our rooks and queens at a standoff until he made a mistake which then led to an even longer delay. Is there any way out of this other than avoiding the situation to begin with?